During morning announcements, your school's principal has announced that your favourite teacher has received an award for teaching. "mrs smith goes out of her way to make learning fun," he says, his voice crackling over the loudspeaker. "mrs smith wears a different hat to teach each subject. she wears a hat with lab equipment to teach science, a hat with nouns and verbs to teach grammar, and a high top hat to teach history."

the sentence that avoid faulty coordination is:

culture, which is well represented in philadelphia, plays a major role including theatre, music, and the visual arts.  

faulty coordination occurs when the writer gives equal importance two different ideas (clauses) which in fact are not equivalent. in order to correct a misplaced clause or idea, the writer can place less important or emphatic ideas in a relative clause as in the previous sentence.  

harlem's  cotton club boasted the talents of duke ellington. singers such as bessie smith and billie holiday popularized blues and jazz vocals. jelly roll morton and louis armstrong drew huge audiences as white americans as well as african americans caught jazz fever.